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resolution(...,DegreeLimit=>...) -- compute only up to this degree

Description

DegreeLimit => n -- keyword for an optional argument used with resolution which specifies that the computation should halt after dealing with degree n.

This option is relevant only for homogeneous modules.

i1 : R = ZZ/101[x,y,z,w];
i2 : M = cokernel matrix {{x*y-z^2,y^2-w^2}}

o2 = cokernel | xy-z2 y2-w2 |

                            1
o2 : R-module, quotient of R
i3 : res(M,DegreeLimit => 1)

      1      2
o3 = R  <-- R  <-- 0
                    
     0      1      2

o3 : ChainComplex
i4 : res(M,DegreeLimit => 2)

      1      2      1
o4 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o4 : ChainComplex

Caveat

One might get some matrix entries of slightly higher degree than requested.

Functions with optional argument named DegreeLimit:

  • compose(Module,Module,Module,DegreeLimit=>...) -- see compose -- composition as a pairing on Hom-modules
  • End(...,DegreeLimit=>...) -- see End -- module of endomorphisms
  • gb(...,DegreeLimit=>...) -- see gb -- compute a Gröbner basis
  • Hom(...,DegreeLimit=>...) -- see Hom -- module of homomorphisms
  • homomorphism'(...,DegreeLimit=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
  • minimalBetti(...,DegreeLimit=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
  • pushForward(...,DegreeLimit=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
  • quotient(...,DegreeLimit=>...)
  • resolution(...,DegreeLimit=>...) -- compute only up to this degree
  • saturate(...,DegreeLimit=>...)
  • syz(...,DegreeLimit=>...) -- see syz(Matrix) -- compute the syzygy matrix

Further information

  • Default value: null
  • Function: resolution -- projective resolution
  • Option key: DegreeLimit -- an optional argument

The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/OldChainComplexes/docs/doc10.m2:53:0.